Nonlinear cooperative control for consensus of nonlinear and heterogeneous systems

In this paper, the consensus problem is considered for nonlinear and heterogeneous systems. Topology of their sensing/communication network is allowed to change in an arbitrary and intermittent way. A matrix-theoretical approach is used to reveal the necessary and sufficient condition of cooperative controllability. The condition is then used to search for cooperative control Lyapunov function (with the same Lyapunov function components) for linear cooperative systems. It is shown that, although finding cooperative control Lyapunov function is often too difficult for nonlinear systems, their cooperative stability can be concluded if the Lyapunov function components satisfy certain differential inequalities along system trajectory. This new result enables an explicit Lyapunov argument with respect to topology changes and a constructive procedure of designing nonlinear cooperative controls for a class of nonlinear and heterogeneous systems. Examples are presented to illustrate effectiveness of the proposed nonlinear cooperative controls.